This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Understand the graph setup. The scale is 2cm to 2 units on each axis, which means 1cm represents 1 unit. The x-axis ranges from -10 to 10. The y-axis ranges from -10 to 10. Draw two perpendicular axes (x-axis and y-axis) on graph paper, marking units according to the scale. Step 2: Plot the original triangle ABC. The coordinates of triangle ABC are given as A(2,2), B(4,7), and C(9,2). Plot these points on the graph and connect them to form triangle ABC. Step 3: Find the image of triangle ABC under an anticlockwise rotation of 90^ about the origin. The rule for a 90^ anticlockwise rotation about the origin (0,0) is (x,y) (-y,x). Applying this rule to the vertices of triangle ABC: A(2,2) A'(-2,2) B(4,7) B'(-7,4) C(9,2) C'(-2,9) Plot these new points A', B', C' and connect them to form the image triangle A'B'C'. The coordinates of the image are: A' = (-2,2) B' = (-7,4) C' = (-2,9) Step 4: Find the image of triangle ABC under a translation by the vector -10 \\ -9 . The rule for a translation by vector a \\ b is (x,y) (x+a, y+b). Here, a=-10 and b=-9. Applying this rule to the vertices of triangle ABC: A(2,2) A''(2+(-10), 2+(-9)) = A''(2-10, 2-9) = A''(-8,-7) B(4,7) B''(4+(-10), 7+(-9)) = B''(4-10, 7-9) = B''(-6,-2) C(9,2) C''(9+(-10), 2+(-9)) = C''(9-10, 2-9) = C''(-1,-7) Plot these new points A'', B'', C'' and connect them to form the image triangle A''B''C''. The coordinates of the image are: A'' = (-8,-7) B'' = (-6,-2) C'' = (-1,-7) Step 5: Find the image of triangle ABC under a reflection in the line y=0 (the x-axis). The rule for a reflection in the x-axis (y=0) is (x,y) (x,-y). Applying this rule to the vertices of triangle ABC: A(2,2) A'''(2,-2) B(4,7) B'''(4,-7) C(9,2) C'''(9,-2) Plot these new points A''', B''', C''' and connect them to form the image triangle A'''B'''C'''. The coordinates of the image are: A''' = (2,-2) B''' = (4,-7) C''' = (9,-2) Send me the next one 📸